Turbine Blades for Reusable Liquid Rocket Engines
(LRE) – Numerical Fatigue Life Investigation
Mateusz T. Gulczyński**, Jörg R. Riccius*, Evgeny B. Zametaev*, Robson H. S. Hahn*,
Günther Waxenegger-Wilfing*, Jan C. Deeken**, Michael Oschwald**
*German Aerospace Center (DLR) – Institute of Space Propulsion
**German Aerospace Center (DLR) – Institute of Space Propulsion, RWTH Aachen University
Im Langen Grund, 74239 Hardthausen am Kocher, Germany
2023 IEEE Aerospace Conference | 978-1-6654-9032-0/23/$31.00 ©2023 IEEE | DOI: 10.1109/AERO55745.2023.10115912
Corresponding author contact: Mateusz.Gulczynski@dlr.de
Abstract—Reusability of LREs in Europe is increasingly
attracting the attention of scientific community and industry
with leading projects such as THEMIS, CALLISTO (reusable
demonstrators for vertical take-off and landing (VTVL))
and Ariane Next – all powered by the reusable cryogenic
Oxygen/Methane
(LOX/LCH4)
engine
“Prometheus”.
To enable
further
expansion
and
cost-effectiveness
of the reusability technology for future liquid rocket engines
(LREs), research on critical engine components such
as turbopumps is crucial. Therefore, within our research
we focus on the turbine blade investigation for reusable LRE
applications including high cycle fatigue (HCF) and low cycle
fatigue (LCF). Validation of defined applied analytical
and numerical techniques is established through the Liquid
Upper stage deMonstrator ENgine (LUMEN)’s, developed
at DLR Lamplodshausen for enhanced expertise in the complete
cycle operation for various engine applications, as well as
to empower validation studies of the operational conditions
to which turbopump components, such as turbine blades,
are subjected.
Turbine blades are exposed to large thermo-mechanical cyclic
strains emerging from an increased temperature driving gas
combined with a fast start-up sequence as well as a large
rotational speed – essential for acquiring high performance and
structural mass efficiency for LREs. Therefore, in addition to
bending & torsion as well as thermal gradient and centrifugal
forces, it is critical to consider creep effects in durability studies.
To forecast the turbine blade fatigue life, analytical (0-D) and
numerical approaches for a selected test case are studied.
Within the proposed method, a BLISK is assessed for the most
severe loading condition considering HCF load by a modified
Goodman method, along with a Coffin-Manson based approach
for LCF contribution. Each operational cycle under constant
maximum loading condition is applied to study the creep effect.
As a result, an enhanced fatigue life prediction method
including both creep and fatigue conditions for a turbine blade
is obtained.
TABLE OF CONTENTS
1. INTRODUCTION ............................................................... 1
2. (0-D) STRUCTURAL ANALYSIS OF THE
TURBOPUMP’S BLADES ..................................................... 2
3. LUMEN’S TURBOPUMP DESIGN
CHARACTERISTICS ............................................................ 4
4. STRUCTURAL 3D FINITE ELEMENT ANALYSIS
METHOD ................................................................................. 5
5. POST-PROCESSING ANALYSIS .................................... 6
6. SUMMARY AND OUTLOOK ........................................... 9
ACKNOWLEDGEMENTS .................................................... 9
REFERENCES....................................................................... 10
BIOGRAPHY ......................................................................... 11
k
1. INTRODUCTION
The turbopumps of a Liquid Rocket Engine (LRE) plays
a vital role in obtaining a high specific impulse and high
thrust-to-weight ratio. To determine the reusability capacity
of the LRE’s turbopump, it is essential to evaluate the main
stresses in the blades to estimate the permissible margins
for the High Cycle Fatigue (HCF) and the Low Cycle Fatigue
(LCF) life of the turbine. At elevated rotational speed,
indispensable to achieve a high power-to-weight ratio, a large
tensile prestressing of turbine blades may be observed.
Over and above that, circumferential flow variations
of the turbine driving gas, ejected from the stator row(s)
of the turbopump, is the source of a severe HCF loading
of turbine blades. As reported in Space Shuttle Main Engine
(SSME) with full admission turbines, as well as in case
of a more recently developed fuel turbopump of the Japanese
LE-5B engine with partial admission turbines, the fatigue life
related failures and cracks in turbine blades can be identified
already during the pre-development and pre-qualification
phases [1], [2], [3], [4]. On that account, within the presented
paper, the generally applicable numerical method is proposed
to evaluate a fatigue life of the turbine blades under severe
loading conditions. As a validation case, a Liquid Upper
Stage deMonstrator ENgine (LUMEN) is employed –
an expander-bleed breadboard engine in the 25kN thrust
class, working on a mixture of liquid oxygen (LOX)
and methane. It enables a complete engine cycle operation
and validation studies for a given operational conditions
to which
turbopump
components
are
subjected.
The LUMEN demonstrator is located at test bench P8.3
in DLR Lampoldshausen, Institute of Space Propulsion.
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2. (0-D) STRUCTURAL ANALYSIS OF THE
TURBOPUMP’S BLADES
Tensile Loads Acting on the Blade Resulting from Centrifugal
The turbopump rotor blades and guide vanes are subjected
to gas-dynamic loads resulting from the pressure distribution
across the blade airfoils. In addition, at increased rotating
speed, the blades masses may induce significant transverse
loads along the curvilinear paths which results from
gyroscopic moments and centrifugal transverse forces [5].
The main loads acting on the turbine blades can be therefore
divided to: static and dynamic loads – arising from
the flowing medium acting on the blade profile, mass loads
induced by centrifugal force, as well as loads triggered
by elastic vibrations of the blades and the entire rotor.
During operations, these loads translate into the following
main stresses [6]:
For a rotor that spins with an angular velocity “ω”,
a differential centrifugal force acting on the blade element
of length dR is calculated in accordance with equation (1):
-
Tensile stresses – resulting from centrifugal forces
2
of the rotating blade mass;
-
Bending stresses – induced by the flowing medium
acting on the blade profile, as well as stresses
resulting from centrifugal forces of the rotating
blade mass along with stresses caused by transverse
vibrations of the blade;
3
-
5
Forces of the Rotating Blade Mass
!! =
"!
#
$
∫%" %&((& + *),*
(1)
The highest centrifugal force is calculated for the crosssection at the root of the blade, at “R0”, with a following
equation:
"!
$
!& = # ∫& %&((& + *),*
(2)
1
Consequently, the centrifugal stresses at the given radius
of the blade are estimated as highlighted in equation (3):
"!
$
"
"
D
)"! +,'#! -'"! .
-' = #( ∫% %&((& + *),* = *#
Tangential stresses – resulting from torsional
moments force induced by the flowing medium
acting on the blade profile, in addition to torsional
moments of the mass forces acting on the blade,
and torsional vibration of the blades active part.
In the Figure 1, the main geometrical parameters
of the LUMEN turbine blade are presented. In the following
sub-sections, the analytical approach for calculating TB main
4
3
2
loads, including:
rotational,
gas pressure,
mechanical 1
is presented [1], [6], [7], [8], [9], [10], [11], [12], [13], [14].
(3)
+
where “.((/* − (!* ) = Φ” represents a cross-section
of the blade airfoil through which the flowing medium
passes. Based on equation (3), the admissible stresses
“kr” acting on the blade material are estimated.
In dependence on the blade material, operating conditions
(e.g. temperature, flowing medium) as well as admissible
stress factor, the elastic growth of the blade is calculated:
)"!
C
'
)"!
'
'&
#
#
Δ2 = *#0 ∫' # ((/* − 3!* )d3! = 1#0 (/2 52 − 3 '% + '%& 8 (4)
$
D
z
Px
dF
Finally, the blade tensile loads resulting from centrifugal
forces of the rotating blade mass are calculated using
a tabular method [6], where a blade is divided into smaller
sections.
C
σ+dσ
dR
Py
F
R1
x
σ
xi
R
dF
σ+dσ
dR
Ri
R0
F
R1
R0
R
R1
Bending Moments Induced by Fluid Medium’s Pressure
x
σ
xi
R
Ri
and The Centrifugal Loads
R0
y
y
y
ω
B
TheB fluid medium passing through the blades generates
dynamic force and force induced by the pressure difference
between a front and rear part of the blade. The force
components, denoted by “Px” and “Py”, as highlighted
in Figure 1, are determined from the equations (5).
δ
X
Axial direction
Axial direction
My
My x
chord
0
X
CG
δ
CG
xchord
Y
chord c
Y
chord c
x
Designed by
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Approved by
Date
gulc_ma
A
Date
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Figure 1 Schematic of the LUMEN TP with a blade
02Drawing+LUMEN_BLISK_MateuszGulczynski
geometry (“R
“R1” – tip radius,
“Rmean” – 1 1 / 1
0” – root radius,
4
3
2
blade centroid radius) (M. T. Gulczyński et al.)
Edition
5
x
Sheet
:% =
*+3
!
*+3
/
*
* )>
;(</ − <* ) + # (%/ =$4
− %* =*4
9
:5 = !# [%/ =/6 (=78 − A) + %* =*4 (=*6 + A)]
(5)
2
Designed by
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Date
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Edition
Sheet
The bending moments are subsequently calculated with
equations (6):
9
$
($-; )!
C9: = ∫; :5 (D − D& ),D = :5 *$
$
$
($-;$ )!
$
*
C>: = ∫; :% (D − D& ),D = :%
The centre of gravity for the LUMEN impulse turbine
profile is calculated as follows (9):
,/ = F?@ − FA34BC;D!E
⎧
,* = F?@ − FFCG!H!3H$C
⎪
⎪
(4IJ)K
+' !
O%,-. = ;5 * 8 (−,/ )> − ;5 * 8 (−,* )>
(6)
(4IJ)K
+' !
⎨
&
= * − *
⎪ 43C4
⎪
L/
⎩F=(
As in case of tensile loads calculations, the bending moments
are calculated using a tabular method, where the blade
is sectioned along the height, similarly to what was presented
in the Figure 1.
2
1
To calculate the total bending moment about the x-axis
in section “i” induced by centrifugal loads, the following
equation (7) is applied:
)
9
'
C%'()*")+ = # E* ∫' # &(F(! − F! (),(
)
C5'()*")+ = # E
*
01(0
which leads to equation (10) for centre of gravity.
PQ = F?M + F
'#
∫'" &(* − *! )RdR
2
To determine the bending stresses in the outermost layers
of the blade, a center of gravity and a moment of inertia
3 blade profile is calculated.
2 The geometrical
for the given
parameters, as highlighted in Figure 1, together with velocity
triangles, as shown in Figure 2, are applied for turbine stress
calculation. The blade profile is approximated with
geometrical figures applied to a blade cross-section, which
allows for a quick estimation of the stress components.
C
As shown in Figure 2, the moments of inertia
of the LUMEN’s impulse turbine blade are calculated
in accordance with a Steiner’s parallel axis theorem:
4
3
2
D
Checked by
(a)
ω
Vr2
B
+,#
+,$
(>* + ?@)" 9 − [ - + " (>" + ?@)" ] − 6; "
(11)
P/
(12)
T+',E0/,$F
(13)
cw2
*
The mean stress -G,&S obtained by this 0D method is the sum
of the centrifugal stress and the stress amplitude:
β2
α1
y=y0
"
-4,&S =
Vb
My
($%'))
α2
V1
β1
cw1
Mx x=x0
CG
atrapezoid
y
V2
9 − 67"
+(
-#4F JCOE!O# = Q $ F
Outlet Velocity
Diagram
Vr1
btrapezoid
1-
Vf2
Vf1
Vb
yCG
htrapezoid
ytrapezoid
ysemicircle
d1
d2
R0
R
R1
R semicricle
RK
R
RB
Inlet Velocity
Diagram
Y
0
B
X
CG
3. = 3.! − 6; " = 8
For the considered
partial admission turbine – the gas
C
bending stress is reduced to zero in the non-admission parts
of the turbine, where stress amplitude -4,&S obtained by this
0D method is half of the max. gas bending stress:
Vb
C
+,#
A change in the angular momentum of the gas
in the tangentialDdirection results in the force that generates
a useful torque and a gas bending moment in the axial
direction. Consequently, a gas bending stress amounts
to the tensile stress – in the leading and trailing edge,
and compressive stress – on the suction side of the blade.
The leading or trailing edge of the root section is often where
the highest stress is located [1], [7], [8], [15].
For the calculations of gas bending and centrifugal stresses,
the velocity triangles schematic is used as highlighted
in Figure 2(b).
where “A” represents the cross-sectional area of the blade,
and “a” and “b” are the distances between given axes.
Py
−
/$
z
Px
($%&'))"
*"
($%')/$$%'$0)
1
(8)
1
3! = 3!! − 67" = 8
As impulse turbine blades are symmetric, the “x=0”
and “C%$ = C% ” and “C5$ = −C5 ” therefore, the bending
stress at any arbitrary point of the section is determined by:
Bending Stresses in the Outermost Layers of the Blade
H% = H%$ − &I*
9 H5 = H5$ − &J*
H%5 = H%$5$ − &IJ
(10)
The turbine moments of inertia about central principal axes
are calculated equations (11) for an impulse turbine type.
D
(7)
"
(9)
B
(b)
-G,&S = -H,&S + -4,&S
Figure 2 Schematic cross-sections of the LUMEN impulse
turbine blade profile, highlighting: (a) blade geometry
with central axis system with bending moments acting
on the blade profile; (b) velocity triangles in front of and
Date(M. T. Gulczyński
Date
Approved
by the blade
behind
et al.)
A
(14)
x
Designed by
Checked by
Date
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gulc_ma
A
Date
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4
3
The main geometric parameters along with operating
conditions applied to the calculations are presented in the
following sections (Table 2, Table 3) [16], [17].
Sheet
02BladeCrossSections_Drawing+LUMEN_BLISK_M
1/1
1
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x
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Sheet
BladeCrossSections_Drawing+LUMEN_BLISK_Mat
1und/ Raumfahrt.
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Zentrum
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3. LUMEN’S TURBOPUMP DESIGN
CHARACTERISTICS
LUMEN Turbopumps Operational Parameters
The study on fuel and oxygen turbopump starts with
preliminary fluid dynamics analysis, where based
on the entrance conditions obtained from the flow path
analysis, the turbine exit gas pressure is established.
The remaining variables (partially presented in Table 1):
velocity ratio, rotational speed of the turbine, diameter,
specific speed, and admission fraction, are calculated
subsequently and utilized to evaluate the turbine efficiency.
As opposed to traditionally used pump fluid for cooling,
LUMEN turbopump employs oil lubricated bearings, which
improves life expectancy as well as increases the adaptivity
of the system. This design choice facilitates investigation
of the turbopump components, including turbine blades
and pumps, without additional need for a major system
modification. The LUMEN’s turbopump consists of a singlestage and single-rotor pressure-compounded impulse turbine.
Both – Fuel Turbopump (FTP) and Oxidizer Turbopump
(OTP) share the similar design, where no static pressure drop
occur and there is no expansion. The design utilizes only one
stage (one stationary nozzle) followed by a row of rotating
blades, what helps in retaining the gas flow velocity, and thus
the kinetic energy at entrance and exhaust. The rotor dynamic
analysis is realized with a DLR in-house tool “ROTAN”,
where parameter variation are performed to estimate
the critical speed of OTP and FTP, along with
solution sensitivity evaluation to the respective parameter
(impeller and turbine weight, bearing and shaft diameter,
shaft sections length etc.) [18]. The schematic representation
of the LUMEN’s architecture along with a cross-section
of the LOx and LNG turbopump is presented in Figure 3.
Table 1 LUMEN’s turbopump operating conditions
Description
!!"#$%&!'",)*+
!&,-.!"$,!"/$&
!01//,%213.$"&,-.!"$
#&,-.!"$,!"/$&
#5,35,)*+
Min
190
2(3!"#$%&',%&)'!)
30
-
Max
550
900
"314
150
Unit
K
K
K
bar
bar
Based on before mentioned values, the turbine blade driving
force is calculated along with remaining input factors, crucial
for the HCF and LCF analysis [1]. The diagram below
(Figure 4) highlights a transient model property applied
to FEM analysis. The pressure and temperature (at a total
inlet condition) are measured before the stator nozzle
resulting in the maximum gas temperature level in the
system. Once the medium has left a stator, the pressure and
temperature decrease due to expansion, resulting in a static
pressure and temperature. Owing to gas dynamics, the rotor
blades will be mostly exposed to static temperature however,
at some locations the shock structure will stagnate the gas,
increasing its temperature to approximately initial value.
Figure 3 LUMEN demonstrator engine schematic
representation combining LOx and LNG Turbopump
cross-sections. (partially adapted from [14], [19], [20])
(M. T. Gulczyński et al.)
Figure 4 LUMEN's turbopump operational sequence
(M. T. Gulczyński et al.)
4
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4. STRUCTURAL 3D FINITE ELEMENT ANALYSIS
METHOD
Although commonly a total temperature after expansion
is lower due to friction losses in the system, in case
of LUMEN the decrease of a total outlet temperature
is negligible throughout all operational conditions.
Therefore, the structural temperature of both stator and rotor
is ceaselessly comparable. In case of the LUMEN
turbopump, operational sequence starts with a chill-down
of the pump followed by a downstream pipeline chill-down.
Subsequently, the turbopump starts-up until the nominal
operational speed is reached. Thereafter, it operates
at constant speed until shut-down and full-stop at the end
of operational time. The change in blade film coefficient
and temperature is primary at nominal operational step.
During a chill-down phase (around 300s), the decrease
of enthalpy in the turbine blade is also insignificant.
Following the chill-down phase, the shaft region is exposed
to a minimum temperature of 280K – therefore, the BLISK
won’t be subjected to cryogenic temperature. In diagram
below (Figure 5), an example of the static temperature
distribution on the blade surface was presented
for a corresponding operational condition to LUMEN.
The surface temperature depends on the evaluated load point
and the time in the transient analysis.
To estimate a critical life of the LUMEN’s turbine blades,
the FEM method is developed incorporating a quasistationary structural 3D Finite Element Model for the HCF
part, along with a transient model to account for LCF effects.
The presented approach is versatile and enables estimation
of a critical life of any turbine blades, including a reusability
potential evaluation. Furthermore, the proposed method
is transferable to large-scale engine’s components
of a similar design. Within presented FEM analysis, three
load steps (LS1 to LS3) provide sufficient input data
for the post-processing HCF and LCF analysis:
• LS1: Transient thermal loading (including start-up phase,
nominal operation and a shut-down of an engine).
• LS2: Additional spin loading (modelling centrifugal forces
under elevated temperature and therefore, representing
the loading of the turbine blade in the non- admission
sections of the turbine).
• LS3: Additional (circumferential) blade driving load in the
admission sections of the turbine (caused by the turbine
driving gas, emitted by the stator row).
For the post processing HCF analysis, the maximum
principal stresses at the maximum loading point for load steps
LS2 and LS3 of the 3D Finite Element analysis are relevant,
whereas in case of the LCF, load step LS1 is essential. The
key geometric parameters of referenced LUMEN’s turbine
blades are presented in Table 2.
Table 2 LUMEN's OTP and FTP input data
Description
Mass of the blade
Radius of the blade centroid
Number of blade driving jets
Figure 5 Example of static temperature distribution
on the blade surface at operational conditions analogous
to LUMEN (M. T. Gulczyński et al.)
Fillet radius (transition between
Parameter
m
Rmean
nstat (OTP)
nstat (FTP)
rfillet
Value
0.0017
0.0635
3
5
0.005
hOTP
hFTP
nblades
!!"
!#"
tOTP
tFTP
c
"$!
0.0093
0.0097
65
69
18
0.00370
0.00406
0.009
246.9
"$#
201.9
#̇
ΘOTP
ΘFTP
%%&'(&)* ,!-
1.046
0.229
0.356
8.19
the disk and the blade)
Blade height
LUMEN’s Turbine Blade Design Features
Number of blades
Input for the calculation of
the blade camber angle
Maximum blade thickness
The LUMEN’s turbopump partial admission turbine blade
design choice arises from the admission degree evaluation
and a trade-off study between the blade geometry, turbine
size, along with a required stator exhaust velocity
and the high cycle fatigue loads. The evolution of radial
clearance ratio and blade height ratio is assessed considering
an admission degree. An increased admission degree
of the LUMEN’s supersonic impulse turbine results
in a uniform flow through the rotor and reduction of the main
losses of its parameters. Concurrently, the fixed meridional
diameter and radial gap influences the blade height which
has to be reduced, what generates more losses related
to leakage at radial clearance [9].
Chord length (OTP &FTP)
Tangential component of
entering stream (whirl velocity)
Corresponding value at exit
of the moving blade
Mass flow rate
Admission degree
Density
Unit
kg
m
m
m
o
m
m
m/s
m/s
kg/s
g/cm3
5
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To allow for flexibility of the model (e.g. follow-on Finite
Element analysis of the remaining operating points
of the LUMEN TP blade) a temperature dependent modulus
of elasticity (as seen in Figure 6) and a temperature
dependent thermal expansion coefficient (as may be seen
in Figure 7) are particularize as an input of the structural
3D Finite Element analysis.
5. POST-PROCESSING ANALYSIS
As part of the turbine blade HCF analysis's initial stage,
the maximum principal stresses of the highest loaded point
of the turbine blade are extracted from load steps LS2 and LS3
of the structural 3D Finite Element analysis. Thereafter,
the mean stress “-G,2S ” (as mean value of the max. principal
stresses of the two 3D FE analysis load steps LS2 and LS3)
and stress amplitude “-4,2S ” (as half of the difference of the
maximum principal stresses, extracted from the two
considered 3D FE analysis load steps LS3 and LS2)
are calculated. As previously stated at the end of Section 2,
the 0D analysis (based on the beam theory) can be
alternatively applied to determine the loads. Finally,
the following equation determines the number of cycles until
failure “RU ” (as suggested in reference [21]):
T0
Modulus o f Elasticity [GPa]
G
RU = .S G
210
(15)
H
W
( V/- E
IG
Contrary to the original Goodman equation, with a stress
amplitude “σX ” being normalised by “σYJ ” at fully reversed
loading conditions “R=-1”, “σZ = 0” and the mean stress
being normalized by the failure stress at constant loading
conditions “R=1”, “σX = 0” to the ultimate tensile stress;
within the herewith demonstrated modified Goodman
equation (15), the “σYJ ” is substituted by the stress amplitude
“σ[ ”at which the assessed turbine blade material fails after
“Nf” cycles at a given mean stress level (“σZ ≠ 0”)
and “σ\]^ ” is replaced by a parameter C’.
Turbine driving gas
temperature
Single blade loading
(in circumferential direction)
130
110
90
70
200
400 600 800 1000 1200
Temperature T[K]
Thermal expansion coefficient
[1/MK]
15,5
15
structural
structural worst-case
worst-case operating
operating
point
point hot-run
hot-run temperature
temperature of
of the
the
LUMEN
Methane
TP
LUMEN
Oxygen
& Methane
TPB
blade
http://www.hightempmetals.co
m/techdata/hitempInconel718d
ata.php
14,5
14
13,5
13
12,5
300 400 500 600 700 800 900 1000
Temperature T[K]
Figure 7 Thermal expansion coefficient of Inconel 718
at the structural worst-case hot-run operating point
of the LUMEN TP (M. T. Gulczyński et al.)
As highlighted above, a temperature dependent material
parameters – both: for modelling elasto- plasticity as well as
for creep were used for the structural Finite Element analyses.
The HCF analysis parameters of Inconel 718 (summarized
in Table 4), are available for ambient temperature only
(in accordance with [21]). (Temperature independent
67
parameters “)%&',!- = 8192 8!”, “ν=0.31” applied)
Table 3 Structural-worst-case operating point blade
loading conditions of the LUMEN’s OTP and FTP
Value
2806
5395
488.36
487.4
49,37
31.97
150
16
The LUMEN turbopumps operate in a temperature ranging
from cryogenic up to driving gas temperature of 500K.
On that account, the material chosen for the turbine blade is
Inconel 718, which offers unique properties for structures
exposed to high pressure and extreme temperatures in a range
of -240°C up to 700°C. Furthermore, a protective oxide layer
provides a significant amount of resistance to oxidation,
thereby increasing turbopump reusability potential.
The structural worst-case (recorded at the location
of the blade leading edge) is established by evaluating the
blade loading conditions for nine operating points for both
LUMEN’s Oxygen and Fuel turbine. Correspondingly with
this data, the operating conditions with the highest amplitude
and the shortest fatigue life are analysed. The main loading
conditions for both turbopumps are highlighted in Table 3.
Parameter
&./0
&1/0
'./0
'1/0
(23&4*),./0
(23&4*),1/0
170
Figure 6 Temperature dependency of the modulus
of elasticity (M. T. Gulczyński et al.)
Turbine Blade’s Material Parameters & Loading Conditions
Loading conditions
Rotational speed OTP
190
Unit
rad/sec
Table 4 Parameters, used for the HCF analysis
HCF analysis parameter
39
49
"9
K
N
Value
7160
-0.1872
1154
Unit
MPa
MPa
6
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FEM Boundary Conditions and Mesh Characteristic
Transient Structural 3D Finite Element Analysis Results
On the left- hand side of Figure 8, the transient structural
boundary conditions applied to the 3D Finite Element model
of the LUMEN OTP and FTP blade are presented. As may
be observed in Figure 8(a), the yellow faces represent
symmetry and convective boundary conditions, where
the total temperature of the turbine driving gas, in the local
coordinate system of the blade, is of maximum 500K.
A blade driving force of “Fsingle = 49.37N” (in case
of the OTP as an example) is distributed as a constant
pressure on the surface highlighted with a red colour
(always acting in the direction normal to the surface).
To account for the LCF effects, a fully transient thermal
analysis is applied to the Finite Element model. In Figure 9
the results for a minimum principal total strain are
highlighted, the minimum principal total strain was found to
be lower than the plasticity limit. Due to moderate operating
temperature (of max 500K), the radial creep deformation
of the turbine blade at the end of the full loading cycle was
found to be insignificant. Conclusively, the creep does not
contribute to the failure of the LUMEN turbine blade under
given loading conditions.
The 3D model is discretized with a tetrahedral or brick shape
elements – 3D 10-Node Tetrahedral Structural, 3D 20-Node
Structural Solid elements. The non-linear model of both OTP
and FTP includes a maximum element size of 0.8mm,
where for the fitting and edge areas, at which maximum stress
and strain values are obtained, the mesh is refined resulting
in an 0.05mm and 0.02mm element size respectively
for OTP, along with 0.1mm and 0.012mm for FTP.
The step size approach for mesh refinement of the blade-hub
transition is used. The meshing reveals a total of 577881
elements and 858714 nodes for OTP, and 196386 elements
and 293313 nodes for FTP. The Finite Element mesh, used
for the 3D analysis of the LUMEN TP blades is shown
in Figure 8(b). The gradual zoom levels – A(2:1) and B(3:1)
– demonstrate the refinement of the Finite Element mesh
in the vicinity of the maximum loading point of the model
(the transition of the blade to the disk at the leading edge
of the blade).
(a)
Figure 9 Min. principal total strain, obtained by fully
transient thermal Finite Element analysis of the LUMEN
FTP blade (M. T. Gulczyński et al.)
The maximum principal stress fields, obtained by load steps
LS2 (combined thermal and centrifugal loading) and LS3
(combined thermal, centrifugal and gas bending loading)
of the 3D FE analysis of the LUMEN TP blade are presented
in Figure 10 and Figure 11 respectively (and for both type of
turbopumps).
Figure 10 Max. principal stress fields, obtained by load
steps LS2 (a) and LS3 (b) of the 3D Finite Element
analysis of the LUMEN Oxygen TP blade
(M. T. Gulczyński et al.)
(b)
Figure 8 (a) Applied boundary conditions (b) Finite
Element Mesh as used for the structural 3D FEA
of the LUMEN Oxygen TP blade and related disk section
(M. T. Gulczyński et al.)
As it may be observed from the numerical analysis, for both
cases LS2 and LS3, the max. principal stresses are recorded
in the proximity of the turbine blade root on the pressure and
the suction side of the blade. The stress is decreasing towards
the tip – which is characteristic of the tensile load.
The centrifugal stress is dependent on the blade material
mass, blade length and the rotational speed.
7
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(a)
(b)
Figure 13 Maximum Principal Stresses for the LUMEN LOx
(a) and Methane (b) TP blade at leading and trailing edge for
load step 2 – LS2 and load step 3 – LS3 (M. T. Gulczyński et al.)
For the numerical analysis, the min. principal stress is equal
to “-H,2S (_`a) = 139C:I” as obtained by the combination
of centrifugal and thermal loading – LS2. In case of combined
thermal, centrifugal & max. gas bending loading – LS3,
the maximum
principal
stress
is
equal
to “5',:; (./0) +54>,8?@,:; (./0) = 1799:;”. In comparison,
within 0D analysis calculated with equations presented
in section 2 and under equivalent loading conditions as well
as with similar material parameters, the centrifugal and gas
bending stress corresponds to “-H,&S (_`a) = 195.4C:I”
and “-#J,G4%,&S (_`a) = 38.29C:I”.
The comparison
of the numerical and analytical 0D results for OTP
is summarized in Table 5.
Figure 11 Max. principal stress fields, obtained by load
steps LS2 and LS3 of the 3D Finite Element analysis of
the LUMEN Fuel TP blade (M. T. Gulczyński et al.)
In Figure 12 and Figure 13, the max. principal stresses
for transient loading in function of time recorded for 475
substeps are shown, combined with a cross-section with max.
principal stress fields for load step 2 (LS2) and load step 3
(LS3). As indicated, for the evaluated operating point,
the max. principal stresses at the leading edge and trailing
edge are of the similar magnitude, what is expected
for a partial admission turbine.
600
Table 5 Structural-worst-case operating point blade
loading conditions of the LUMEN Oxygen TP
FTP leading edge
FTP trailing edge
OTP leading edge
Max. Principal Stress, [MPa]
500
OTP trailing edge
Nomenclature
Parameter
3D FE
analysis
Cyclic stress
Stress
amplitude
Mean stress
5'A'*3'
0D value
0D beam
theory
Unit
40.4
38.3
MPa
5%
5?
20.2
19.15
MPa
5%
58
158.9
214.55
MPa
26%
────────
3D value
The further comparison of analytical and numerical methods
for FTP, presented in Table 6, utilizes a 0D calculation
approach introduced in publication [7]. This was conducted
for additional accuracy evaluation of the analytical method
previously proposed.
400
300
200
Table 6 Structural-worst-case operating point blade
loading conditions of the LUMEN Methane TP
(0D calculations applied in accordance with methodology
presented in [1] and [7] for accuracy comparison)
100
0
1,0
1,5
2,0
2,5
3,0
3,5
4,0
Nomenclature
Parameter
3D FE
analysis
Cyclic stress
Stress
amplitude
Mean stress
5'A'*3'
Unit
26
18
MPa
30%
5?
13
9
MPa
30%
58
549
396
MPa
28%
Time, [s]
Figure 12 Maximum Principal Stresses for the LUMEN
OTP & FTP blade at leading and trailing edge for load
step 2 – LS2 and load step 3 – LS3 (M. T. Gulczyński et al.)
0D value
0D beam
theory
────────
3D value
8
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Results Outline
17 trillion cycles for FTP. To increase the performance
and efficiency of the engine, a higher temperature
in the turbomachinery component is inevitable. Therefore,
it is especially important for the future reusable applications,
that the turbomachinery components are evaluated
considering the operating temperature. The assessed
turbopump material operates within the hot-run temperature
range of approximately 500K – where for Inconel 718
the yield strength within this temperature range is as high
as “syield, Inconel718 atT=500 K =1100MPa” [22]. Therefore, the life
reduction due to thermal loading is found to have
an insignificant influence.
The OTP stresses obtained from the 0D beam theory
suggested in section 2 were found to be approximately 26%
higher than the stresses received through the 3D Finite
Element Analysis. In comparison, the stresses calculated with
previously developed methods [7], differs from FEM
by 28%. The inaccuracy in calculations between 0D
and FEM, could be on account of stresses being calculated
in radial direction of the turbine (equaling to the height
direction of the turbine blade) for former, in contrast
to max. principal stresses extracted for latter.
The mean stress (green and blue line) and the stress amplitude
(violet line) as obtained by the 3D Finite Element analysis
in relation to the test data given in Reference [21] (blue
circles) used for fitting the HCF analysis parameters &b , ^b
and P b (as given in Table 4) is visualized in Figure 14.
The large gap between the (violet) stress amplitude line
and the (blue) circles, indicates that the HCF analysis of the
operating point of the considered turbine blade requires
a large extrapolation of experimental HCF data. In order to
visualize the HCF analysis according to equation (19),
HCF life iso lines for 100 Mcycles, 10 Gcyles and 1 Tcycle
were calculated by this equation and additionally included in
Figure 14 (combined with Haigh diagram for Inconel 718).
6. SUMMARY AND OUTLOOK
Within presented paper, two structural analysis methods were
compared: 0D analysis – based on the beam theory,
and a transient 3D Finite Element method. The analytical
approach was found to be in an acceptable margin with
the respective results, obtained by the 3D FE analysis.
The post-processing transient HCF/LCF analysis, based
on the max. principal stress values of the above-mentioned
3D Finite Element analysis, resulted in a fatigue life
of 17 trillion cycles before failure for Oxygen Turbopump,
and 13 trillion cycles to failure for a Methane Turbopump.
Furthermore, for the considered reference turbine blade,
the HCF (at the leading edge of the reference turbine blade)
seems to be dominant in relation to LCF failure (at the trailing
edge of the turbine blade). Due to the relatively moderate hotrun temperature (500K) of the reference turbine blade, creepcaused failure is fully negligible.
The foreseen improvements of the presented methods will
include further developed transient analysis and a damped
vibration of the turbine blade in the non-admission sections
of the turbine. Furthermore, an extended fatigue life analysis
with implementation of a damage accumulation method
presented in [23], [24], for improved accuracy of the LCF
models is envisage. For the post-processing HCF/LCF
evaluation, additional tests are foreseen outside LUMEN
demonstrator, where LCF effects at increased operating
temperatures can be validated. What’s more, the study
of the turbopump life reduction due to elevated temperatures
is envisioned, which shall prove the versatility of the hereby
presented methods when evaluating turbopumps working
in wider spectrum conditions, including large scale
turbopump turbines operating within higher temperature
range. The lessening blade’s life influenced by effects such
as multiaxial fatigue – combined HCF and LCF ([25]), creep
or corrosion, will be further evaluated with developed models
for different engine applications.
Figure 14 Visualization of the structural-worst-caseoperating point of the LUMEN Oxygen and Methane TP
blade (crossing point of the green and the violet line)
in relation to HCF test data (blue circles). OTP and FTP
vertical lines represents the mean stress value
at maximum loading position (M. T. Gulczyński et al.)
ACKNOWLEDGEMENTS
The project leading to this paper has received
funding from the European Union’s Horizon 2020
research & innovation programme under the Marie
Skłodowska-Curie grant agreement No 860956.
Due to the low stress amplitude of just 20 MPa, the HCF life
of the LUMEN TP blades, as predicted by equation (6), is as
high as RU = 17 trillion cycles before failure for OTP and
9
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[14]
R. H. S. Hahn, M. T. Gulczyński, E. Kurudzija, K.
Dresia, G. Waxenegger-Wilfing, and J. Deeken,
“LUMEN Evolution for Lunar Lander Propulsion”
[15]
W. Zhang, Failure characteristics analysis and fault
diagnosis for liquid rocket engines. 2016. doi:
10.1007/978-3-662-49254-3.
[16]
R. Kumar et al., “Thermo-mechanical analysis and
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10.1016/j.applthermaleng.2020.115700.
[17]
R. I. Thamizh, R. Velmurugan, and R. Jayagandhan,
“Finite element analysis of metal matrix composite
blade,” IOP Conf. Ser. Mater. Sci. Eng., vol. 152,
no. 1, 2016, doi: 10.1088/1757-899X/152/1/012008.
[18]
T. Traudt et al., “LUMEN Turbopump - Design and
Manufacturing of the LUMEN LOX and LNG
Turbopump components,” 2019.
[19]
T. Traudt et al., “LIQUID UPPER STAGE
DEMONSTRATOR ENGINE (LUMEN):
COMPONENT TEST RESULTS AND PROJECT
PROGRESS,” in Space Propulsion Conference
2022, 2022, no. SP2022_00362.
[20]
J. Deeken, M. Oschwald, and S. Schlechtriem,
“LUMEN DEMONSTRATOR – PROJECT
OVERVIEW,” no. March, 2021.
[21]
Г. Г. Гахун and . и др (сост.), КОНСТРУКЦИЯ И
ПРОЕКТИРОВАНИЕ ЖИДКОСТНЫХ
РАКЕТНЫХ ДВИГАТЕЛЕЙ. Москва
Машиностроение, 1989.
M. Bruchhausen et al., “Impact of hydrogen on the
high cycle fatigue behaviour of Inconel 718 in
asymmetric push-pull mode at room temperature,”
Int. J. Fatigue, vol. 70, pp. 137–145, 2015, doi:
10.1016/j.ijfatigue.2014.09.005.
[22]
Robson H. S. Hahn, Jan C. Deeken, Tobias Traudt,
Michael Oschwald, Stefan Schlechtriem, and
Hideyo Negishi, “LUMEN Turbopump Preliminary Design of Supersonic Turbine,”, 2019.
Y. Zhang et al., “Microstructures and properties of
high-entropy alloys,” Prog. Mater. Sci., vol. 61, no.
November 2013, pp. 1–93, 2014, doi:
10.1016/j.pmatsci.2013.10.001.
[23]
M. T. Gulczyński, J. R. Riccius, G. Waxeneggerwilfing, J. C. Deeken, and M. Oschwald,
“Numerical Fatigue Life Analysis of Combustion
Chamber Walls for Future Reusable Liquid Rocket
Engines (LREs) Applications,” 2022, no. SP2022.
[24]
M. T. Gulczyński, J. R. Riccius, G. Waxeneggerwilfing, J. C. Deeken, and M. Oschwald,
“Combustion Chamber Fatigue Life Analysis for
Reusable Liquid Rocket Engines (LREs),” 2023,
AIAA SciTech Forum 2023, pp. 1-16.
[25]
J. R. Riccius, E. B. Zametaev, and L. J. Souverein,
“HCF, LCF and creep life analysis of a generic LRE
turbine blade,” AIAA Sci. Technol. Forum Expo.
AIAA SciTech Forum 2022, pp. 1–10, 2022, doi:
10.2514/6.2022-0796.
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Z. Dżygadło, M. Łyżwiński, J. Otyś, S. Szceciński,
and R. Wiatrek, Napędy Lotnicze - Zespoły
Wirnikowe Silników Turbinowych. Wydawnictwo
Komunikacji i Łączności, 1982.
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J. Lipka, Wytrzymalosc Maszyn Wirnikowych. Wyd.
Naukowo-Techniczne Warszawa, 1967.
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M. T. Gulczyński et al., “Numerical Turbine Blade
Fatigue Life Analysis for Reusable Liquid Rocket
Engines (LREs) Applications,” 2022, no. 9TH
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(EUCASS), doi: 10.13009/EUCASS2022-6150.
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Rogers, P. V. Straznicky, and A. C. Nix, Gas
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Available: https://elib.dlr.de/148758/
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BIOGRAPHY
Mateusz T. Gulczyński is a Research
Scientist in Rocket Engine Systems
Department at the Institute of Space
Propulsion at German Aerospace
Center (DLR) and a PhD Student
for Reusable
Space
Propulsion
Systems at RWTH Aachen University.
His area of activity enfolds rocket
engine design and operation with
a specific focus on methods for fatigue life estimation
of highly loaded rocket engine components into low order
tools for rocket engine cycle modeling.
Jörg R. Riccius received his Ph.D.
degree in civil engineering from KIT
Karlsruhe, boosted by a 2-year postdoc position at the department
of aeronautics of the Imperial College
London. He is the technical leader
of the
Structures
team (inside
the Rocket Propulsion department) at
the German Aerospace Center (DLR).
His research is focused on method development for (thermal
and structural) FE and fatigue life analyses of liquid rocket
engine (LRE) components including validation by dedicated
LRE sub-component tests.
Evgeny B. Zametaev received his
engineering
education
from
the MINT (Moscow Physic Technic
Institute) in 1983. Till 2001
he worked at the CADB (Chemical
Automatic
Design
Bureau)
in Voronezh, Russia, as a leader of
the FE analyses group. In 19971998, he participated in the Russian
Teams in the Space-Shuttle-Nozzle-Projects. Since 2001
he has worked at the DLR Institute of Space Propulsion,
Department of Rocket Propulsion Technology, Structure
Group. His research is focused on structure and thermal
FE analyses of the Rocket engines: turbopump, chamber,
nozzle and other elements of the LRE.
for L75 project. Since November of 2015 is working
at German Aerospace Center as part of System Analysis
group as well as in the LUMEN Project, especially
in the Turbopump development and test front as well
as in the Transient analysis system.
Günther
Waxenegger-Wilfing
received
his
Ph.D.
degree
in theoretical physics from the
University of Vienna. He is currently
a professor for aerospace computer
science
at
the
University
of Würzburg and at the same time
head of the system analysis and control research group
at the Institute of Space Propulsion at the German
Aerospace Center (DLR). His main research interest
is the application of machine learning and artificial
Intelligence methods to problems in aerospace with
a specific focus on rocket engine design and control
as well as autonomous spacecraft operation.
Jan C. Deeken received his Diploma
degree in mechanical engineering from
RWTH Aachen University in 2007
and joined DLR Institute of Space
Propulsion
in
Lampoldshausen
the same year. He received his Ph.D.
title for his work on porous injectors
for high-pressure rocket combustion
chambers in 2014 from Stuttgart University. Since 2020 he
is the acting department head of the newly found rocket
engine system department at the Institute of Space
Propulsion. Together with his coworkers in three research
groups he is working on topics ranging from thrust chamber
design, turbopump design, system analysis and control for
cryogenic liquid rocket engines. In 2022 he took over
the Chair of Space Propulsion at the Institute for Jet
Propulsion and Turbomachinery at RWTH Aachen
University.
Michael Oschwald is Coordinator
for Rocket Propulsion at the Institute
of Space Propulsion at the German
Aerospace Center (DLR) and professor
for Space Propulsion of the RWTH
Aachen University. His fields of activity
cover all aspects of rocket engine design
and operation with a specific focus on
cryogenic propulsion. His department
at DLR has a long heritage in
experimental investigations of high pressure combustion,
heat transfer, combustion instabilities, and expansion
nozzles. In parallel to the experimental work numerical tools
are developed in his department to predict the behavior of
rocket engines and their components.
Robson H. S. Hahn graduated
in Physics at Estate University
of Mato Grosso do Sul (UEMS)
in 2007, received his Master
Degree in Space Propulsion by
Technological
Institute
of
Aeronautics (ITA) and Moscow
State Aviation University (MAI)
in 2010 on topics of Liquid Propellant Rocket Engines.
Work in Research and development of LPRE at Institute
of Aeronautics and Space (IAE), from 2008 to 2015
and from 2013 to 2015 was manager of combustion system
11
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